Bivariate nonparametric estimation of the Pickands dependence function using Bernstein copula with kernel regression approach

Ahmadabadi, Alireza; Ucer, Burcu Hudaverdi

doi:10.1007/s00180-017-0750-2

Cited by 7 publications

(4 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence these estimators do not necessarily provide a Pickands function, they have to be further constrained; as pointed out in Rojo et al (2001), who also provided some estimators satisfying the convexity condition and demonstrated the strong uniform convergence. Ahmadabadi and Ucer (2017) introduced a new estimator for the Pickands function based on Bernstein copula and kernel regression. However, its inclusion in the Archimax copula estimation has not yet been studied, while in Kiriliouk et al (2018) the empirical beta copula was used.…”

Section: Estimating Archimax Copulaementioning

confidence: 99%

Copulae: An overview and recent developments

Größer

Okhrin

2021

WIREs Computational Stats

View full text Add to dashboard Cite

Over the decades that have passed since they were introduced, copulae still remain a very powerful tool for modeling and estimating multivariate distributions. This work gives an overview of copula theory and it also summarizes the latest results. This article recalls the basic definition, the most important cases of bivariate copulae, and it then proceeds to a sketch of how multivariate copulae are developed both from bivariate copulae and from scratch. Regarding higher dimensions, the focus is on hierarchical Archimedean, vine, and factor copulae, which are the most often used and most flexible ways to introduce copulae to multivariate distributions. We also provide an overview of how copulae can be used in various fields of data science, including recent results. These fields include but are not limited to time series and machine learning. Finally, we describe estimation and testing methods for copulae in general, their application to the presented copula structures, and we give some specific testing and estimation procedures for those specific copulae.

show abstract

Section: Estimating Archimax Copulaementioning

confidence: 99%

Copulae: An overview and recent developments

Größer

Okhrin

2021

WIREs Computational Stats

View full text Add to dashboard Cite

show abstract

“…In the end of the 20th century, this theory was rapidly developing at home and abroad. Since the 1980s, this theory has been widely applied to insurance, banking business, machine diagnostic system, even to buildings fields, traffic controlling, space technology and so on [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. General distribution algorithm can't build suitable multivariate JDF (joint distribution function) which can expresses the relationship between it and marginal single distribution functions.…”

Section: Introductionmentioning

confidence: 99%

Copula Function method of the kinematic accuracy of cylindrical roller bearing

Xue

et al. 2022

Preprint

View full text Add to dashboard Cite

The kinematic accuracy of cylindrical rollers bearing isn’t only influenced by the size and form precision of its parts, but also more influenced by the cooperation among them. For cylindrical rollers bearing, the main indices of the kinematic accuracy are the ending beat and the radial run out of bearings. There must be dependent relationship between the cooperative action among the parts of bearings and the ending beat or the radial run out of bearings. This relationship is hardly expressed by mathematical formula. However, because the parts dimension deviation and the run out of bearings follow statistic law and have their distribution characteristics, while the copula joint distribution function can connect the run out of bearings with multiple parts dimension accuracy. The copula function is introduced to analyze the dependent relationship between bearing parts cooperative action and its kinematic accuracy. Based on the copula function of statistic theory, the kinematic accuracy of bearings can be forecast by parts geometric accuracy.

show abstract

“…In the end of the 20th century, the theory and methods of copula were rapidly developing at home and abroad. Since the 1980s, this theory has been widely applied to insurance, banking business, machine diagnostic system, even to buildings fields, traffic controlling, space technology and so on [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. General distribution algorithm can't build suitable multivariate JDF (joint distribution function) which can expresses the relationship between it and marginal single distribution functions.…”

Section: Introductionmentioning

confidence: 99%

Copula method of the kinematic accuracy of cylindrical roller bearing

Xue

2021

Preprint

View full text Add to dashboard Cite

The kinematic accuracy of cylindrical rollers bearing isn’t only influenced by the dimensional and form precision of its parts, but also more influenced by the cooperation among them. For cylindrical rollers bearing, the main indices of the kinematic accuracy are the ending beat and the radial run out of bearings. There must be dependent relationship between the cooperative action among the parts of bearings and the ending beat or the radial run out of bearings. This relationship is hardly expressed by mathematical formula. However, because the parts dimension deviation and the run out of bearings follow statistic law and have their distribution characteristics, while the copula joint distribution function can connect the run out of bearings with multiple parts dimension accuracy, the copula function is introduced to analyze the dependent relationship between bearing parts cooperative action and its kinematic accuracy. Based on the copula function of statistic theory, the kinematic accuracy of bearings can be forecast by parts geometric accuracy.

show abstract

Bivariate nonparametric estimation of the Pickands dependence function using Bernstein copula with kernel regression approach

Cited by 7 publications

References 13 publications

Copulae: An overview and recent developments

Copulae: An overview and recent developments

Copula Function method of the kinematic accuracy of cylindrical roller bearing

Copula method of the kinematic accuracy of cylindrical roller bearing

Contact Info

Product

Resources

About